Characterization of sandstone reservoirsusing Poisson impedance inversionRitesh K. Sharma and Satinder ChopraArcis Seismic Solutions, TGS, Calgary, Canada

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We demonstrate the application of Poisson impedance (PI)inversion for characterizing sandstone reservoirs encased inshale, when the impedance contrast between them is verysmall. Poisson Impedance is defined as the difference betweenthe P-impedance (IP) and a scaled version of the S-impedance(IS), where the scalar (c) can be determined from the slope ofthe regression line between IP and IS. Using well data, if the PIcurve is correlated with the Gamma Ray (GR) curve, theporosity (f) curve, or the water saturation curve for differentvalues of c, it is possible to determine the maximum correlationcoefficient in each case. The c value corresponding tothe maximum correlation coefficient for GR is used tocompute another attribute called lithology impedance(LI). Similarly, fluid impedance (FI) can be computedusing the c value that corresponds to the maximumcorrelation coefficient for the porosity (f) curve. Thecross-plot between LI and GR shows the advantages ofLI in distinguishing sandstone from shale. Pore contentis predicted using the linear relationship exhibited onthe cross-plot of FI versus f.

Introduction

The increasing demand for oil and gas motivatesgeoscientists to not only explore new reservoirs but totry and characterize the existing ones in a robust way

as well. One of the challenges in doing so is to be able todifferentiate lithology and fluids in the reservoir. Rockphysics constants such as, bulk modulus (k), shear modulus(m), Young’s modulus (E), Lambda-rho (lr), and Mu-rho (mr)attributes are commonly used for discriminating lithology(sandstones versus shale) or fluids (gas, oil, water). P-wavevelocity (VP) and S-wave velocity (VS) or P-impedance (IP)and S-impedance (IS) plus density (r) are prerequisites for thecomputation of all the attributes mentioned above. Over thelast few years, pre-stack seismic inversion has been used to

Figure 1. Target Correlation Coefficient Analysis (TCCA) for (a) Lithologyimpedance. (b) Fluid impedance. The c-value in (a) is 2.78 and in (b) is 1.75.These values are used for computing LI and FI.

Figure 2. (a) Cross-plot of LI versus GR color coded with GR. Different clusters corre-sponding to shale and sand stone are noticed here. The red polygon corresponds to low GRand LI. Points corresponding to high GR and LI are enclosed by the blue polygon. (b) Theback projection of these polygons on well curves reveals that points from the red polygoncome from the Halfway sandstone while shale exhibits the points from the blue polygon.

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estimate these attributes. This seismic inversion yields IP, IS,Poisson’s ratio (via VP/VS ratio) and density. The robust deter-mination of density from seismic requires really long offsets andnoise-free data which is seldom available. In order to avoid thisstringent requirement of density, we usually compute it as itsproduct with other attributes such as lr, mr, kr� and Er. Finally,the cross-plotting pair of these attributes is used for discrimi-nating lithology and fluid content.

The method

It is usually noticed that the cross-plotting of IP versus IS for datafrom a thin zone enclosing a gas sand reservoir yields a cluster ofpoints corresponding to gas sand somewhat separated from thecluster of points coming from the background shale. The separa-tion between these clusters depends on the impedance contrastbetween the litho-fluid and background lithology. Moreover, for

enhanced separation between gas sand and background shale,another attribute combination such as the lr - mr cross-plot is used.This cross-plot exhibits more separation as gas sand shows lowervalues of lr and higher values of mr than the background shale.

On these cross-plots, it may be difficult to discriminate the litho-fluid distribution where clusters are not completely separated.But in such cases, rotating the axes to be parallel with the trendswould ensure a distinct discrimination of the litho-fluid distri-bution. This rotation can be achieved by computing an inter-esting attribute namely Poisson impedance (Quakenbush et al.,2006). It incorporates the information of Poisson’s ratio anddensity. Mathematically, it can be expressed as PI = IP – cIS wherec is the term that optimizes the rotation. The value of c needs tobe determined from the regression line of the cross-plot of the IPand IS logs for the wet trend. The inverse of the slope can be usedas the c value. Additionally, the target correlation coefficient

analysis (TCCA) method (Tian et al., 2010) can be usedto calculate c.

The automatically generated correlation coefficientbetween the PI curve with different c values and theGamma Ray and porosity curves is computed. The cvalue corresponding to the maximum correlation coef-ficient for GR is used to compute an attribute thatwould emphasize lithology and so is known aslithology impedance (LI). Similarly, fluid impedance(FI) is computed using a c value that corresponds to themaximum correlation coefficient for the porosity curve(Direzza et al., 2012). Cross-plots between LI and GRcan now be constructed that show the advantage of LIin distinguishing sandstone from shale. Fluid contentis predicted using the linear relationship exhibited onthe cross-plot of FI versus f.

Examples

In the present study, we demonstrate the application ofthe above methodology for characterizing the sand-stone of Halfway and Doig Formations of northeasternBritish Columbia, Canada. The Doig Formation isgenerally a mixture of shale and siltstones. The lowerlevels of the Doig Formation are radioactive, whereasthe upper levels are not. The contact between the Doigand Halfway Formations is more problematic but isgenerally assigned to the top of the uppermost promi-nent shale interval below the distinct and widespreadsandstone facies assigned to the Halfway sandstone.However, in places relatively thick sandstone in theUpper Doig Formation are developed near or immedi-ately below the Halfway Formation sandstone, and thisposes a problem in assigning the contact between thetwo formations. Locally, tidal channels, which are partof the Halfway shore-face cut into the Doig siltstonesand shale, and again create difficulty in distinguishingthe two formations.

In this study, we automatically calculate the correlationcoefficients between the PI curve with different c-valuesversus the GR curve and the porosity (f) curve. Thiscorrelation of PI with GR is shown in Figure 1a. Themaximum correlation coefficient reached in Figure 1a for

Figure 3. (a) Cross-plot of FI versus � color coded with �. Different clusters corresponding to shaleand sandstone are noticed here. The red polygon corresponds to high � and FI. Points correspon-ding to low � and FI are enclosed by the blue polygon. (b) The back projection of these polygons onwell curves reveals that points from the red polygon come from the Halfway sandstone while shaleexhibits the points from the blue polygon.

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the c-value is 2.78 (cc=0.678). Similarly, the correlation of PI with fis illustrated in Figure 1(b). The c-value 1.75 (cc=-0.875) correspon-ding to the maximum correlation of the PI with the porosity curveis noticed. Thus, Poisson impedance attributes, namely, Lithologyimpedance (LI) using equation IP - 2.78*IS, and Fluid impedance(FI) using equation - (IP - 1.75*IS) can be derived. They are usefulbecause of their sensitivity to lithology and porosity respectively.The cross-plot of LI versus GR is shown in Figure 2a. On this the redpolygon encloses the points having low LI and GR while pointscorresponding to high LI and GR are enclosed by the blue polygon.The back projection of these polygons on well-log curves is shownin Figure 2b. Notice that the points corresponding to red polygonare coming from the Halfway sandstone while the shale formationis highlighted by the points coming from blue polygon. Thus, thecross-plot of LI versus GR shows the advantage of LI in distin-guishing sandstone from shale. The cross-plot of FI versus f isshown in Figure 3a and it shows that we can predict the porosityinformation from its “linear relationship”. Two polygons corre-sponding to high and low (FI, f) are considered on this cross-plot.The back projection of these as shown in Figure 3b reveals that thehigh (FI, f) corresponds to Halfway sandstone while shale exhibitslow (FI, f).

Poisson impedance from seismic data

The workflow for Poisson Impedance (PI) involves computing IPand IS volumes from pre-stack seismic data. For computing theseprerequisites, simultaneous inversion is performed. This inversionmethod facilitates the estimation of the P- and S-impedancedirectly from the pre-stack seismic gathers, without first estimatingthe P- and S-reflectivities from pre-stack seismic data and then

transforming them to impedance. In this inversion, we start withan initial low-frequency model and generate synthetic traces fromit. For generating synthetic traces, angle dependent wavelets arecomputed statistically from the input data by assuming it to be zerophase, and are then convolved with the modeled reflectivities.Further, the model impedance value is changed in such a mannerthat the mismatch between the modeled angle gather and the realangle gather is minimized in a least squares sense. Having IP and ISvolumes, LI and FI are then derived using equations derived fromwell log curves analysis.

Figure 4a shows the horizon slice of LI taken at the Halfwayhorizon. The same horizon slice of FI is shown in Figure 4b. Fromthe analysis carried out at well log curves, it was concluded thatlow LI and high FI correspond to the sandstone; with that in mindwe have mapped the presence of sandstone, laterally, on theseslices as indicated with the black outline. Similarly, the horizonslices of LI and FI are shown in Figures 5a and 5b, respectively,when the Halfway horizon is shifted 30 ms below. It is noticedhere that the presence of sandstone disappears on these slices.

Conclusions

In conclusion, PI is very favorable attribute for sandstone reservoircharacterization. Using TCCA method, we can derive two attrib-utes of PI namely Lithology Impedance (LI) and Fluid Impedance(FI). The results on log data show that sandstone and shale can bewell distinguished by LI. Also FI provides a potential pore spacecontent identification. Integrating with geological, petrophysical,and well test data, the sandstone reservoirs can be characterizedproperly and new prospect can be identified directly. R

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Figure 4. Horizon slices of (a) Lithology Impedance and (b) Fluid Impedance over the 10 ms window centered at the Halfway horizon. As low LI and high FIcorrespond to the sandstone; we have mapped the presence of sandstone, laterally.

Figure 5. Horizon slices of (a) Lithology Impedance and (b) Fluid Impedance overthe 10 ms window centered at the Halfway horizon when it is shifted 30 ms below.The disappearance of sandstone laterally is noticed.

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Ritesh Kumar Sharma is from a small townin India. He received his B.Sc. degree fromC.C.S. University Meerut, India in 2004 andhis Master’s in applied geophysics fromIndian Institute of Technology, Roorkee, Indiain 2007. In 2008, he came to Calgary to pursuehis studies at the University of Calgary, withCREWES group, and received M.Sc. in

geophysics in 2011. Before coming to Calgary, he worked withthe Vedanta group, Udaipur, for one year as a geophysicist. Hejoined Arcis Seismic Solutions in 2011 and is still working thereas a reservoir geoscientist. His areas of interest include reservoircharacterization, seismic imaging and inversion.

Satinder Chopra received M.Sc. and M.Phil.degrees in physics from Himachal PradeshUniversity, Shimla, India. He joined the Oiland Natural Gas Corporation Limited(ONGC) of India in 1984 and served there till1997. In 1998 he joined CTC Pulsonic atCalgary, which later became Scott Pickfordand Core Laboratories Reservoir Technologies.

Currently, he is working as Chief Geophysicist (Reservoir), atArcis Corporation, Calgary. In the last 28 years Satinder hasworked in regular seismic processing and interactive interpreta-tion, but has spent more time in special processing of seismic datainvolving seismic attributes including coherence, curvature andtexture attributes, seismic inversion, AVO, VSP processing andfrequency enhancement of seismic data. His research interests

focus on techniques that are aimed at characterization of reser-voirs. He has published 8 books and more than 270 papers andabstracts and likes to make presentations at any beckoning oppor-tunity. He is the Editor of the Geophysical Corner in the AAPGExplorer, the past Chief Editor of the CSEG RECORDER, the pastmember of the SEG ‘The Leading Edge’ Editorial Board, and theEx-Chairman of the SEG Publications Committee.

He received several awards at ONGC, and more recently hasreceived the AAPG George C. Matson Award for his paper enti-tled ‘Delineating stratigraphic features via cross-plotting ofseismic discontinuity attributes and their volume visualization’,being adjudged as the best oral presentation at the 2010 AAPGAnnual Convention held at New Orleans, the ‘Top 10 Paper’Award for his poster entitled ‘Extracting meaningful informa-tion from seismic attributes’, presented at the 2009 AAPGAnnual Convention held at Denver, the ‘Best Poster’ Award forhis paper entitled ‘Seismic attributes for fault/fracture charac-terization’, presented at the 2008 SEG Convention held at LasVegas, the ‘Best Paper’ Award for his paper entitled ‘Curvatureand iconic Coherence–Attributes adding value to 3D SeismicData Interpretation’ presented at the CSEG Technical Luncheon,Calgary, in January 2007 and the 2005 CSEG MeritoriousServices Award. He and his colleagues have received the CSEGBest Poster Awards in successive years from 2002 to 2005.

He is a member of SEG, CSEG, CSPG, CHOA (Canadian HeavyOil Association), EAGE, AAPG, APEGGA (Association ofProfessional Engineers, Geologists and Geophysicists ofAlberta) and TBPG (Texas Board of Professional Geoscientists).

TTI…Continued from Page 64

Answers for “Blast from the Past” in Tracing the Industry

In the picture (in no particular order) are Oliver Kuhn, Norbert Bernoth, Leo Macht, John Simmonds, Bob Macht, Steve Fuller, BobSouth and Carmine Militano. Some people might recognize Kent Fargey and Vince Sisko who used to work in the industry.

Acknowledgements

We thank Arcis Seismic Solutions, TGS for allowing us to presentthis work.

ReferencesDirezza, A., Andika, I. K. and Permana, A., 2012, The application of Poisson ImpedanceInversion for Sandstone Reservoir Characterization in the Lower Talang, Akar Formation:AAPG International Convention and Exhibition, Singapore, 16-19 September 2012.

Quakenbush, M., B. Shang, and C. Tuttle , 2006, Poisson impedance: The LeadingEdge , 25, no. 2, 128–138.

Tian,L., D.Zhou,G. Lin and L. Jiang, 2010, Reservoir prediction using PoissonImpedance in Quinhuangdao, Bohai Sea, 80th Annual International Meeting, SEG,Expanded Abstracts, 2261-2264.